A proof of any form requires logical reasoning. Logical reasoning ensures that the conclusions you reach are true-if the rest of the statements in the argument are true.

Logic
CONDITIONAL: If p then q or ( P => Q)
deductive reasoning/deduction: The process of drawing conclusions by using an argument.
If then statements!
If a car is a corvette then it's a Chevrolet. This statement is a conditional statement.
In a conditional the part following the word if is the hypothesis. The part following the word then is the conclusion.
When you interchange the hypothesis and the conclusion of a conditional the new conditional is called a converse of the original conditional.
An "IF" "THEN" statement is called a "conditional statement"
  • All definitions can be interpreted "forward" and "backward"
If a car is a Chevrolet then the car is a Corvette.

IF-THEN TRANSITIVE PROPERTY
-
Given: If A then B, and if B then C.
- You can conclude: If A then C.
Counterexample - an example which proves that a statement is false

Perpendicular: two lines that intersect to form a right angle.

external image perpendicularBisector1.gif perpendicular angle
Biconditional Statement: a logical statement containing "If and only If".
  • a biconditional is equivalent to writing a conditional statement and its converse.
A biconditional statement can be true or false. To be true, both the conditional and its converse must be true. All definitions are biconditional statements.

Example: If cats freak, then mice frisk
If sirens shriek, then dogs howl
If dogs howl, then cats frisk

Solution: If sirens shriek, then dogs howl
If dogs howl, then cats freak
If cats freak, then mice frisk